Math Problem Statement
fill out this graph correctly
Fill out this graph correctly
Solution
Let's fill out the missing values in the tables for each equation based on the information provided.
Equation 1:
Given:
- , (already filled)
- , (already calculated in the formula box)
- , (already filled)
To complete:
Let's select an additional value, such as , and calculate .
-
For : So, when , .
-
Another value, for : So, when , .
Now, the completed table for will be:
0 | 3 |
6 | 7 |
10 | 12 |
-3 | 1 |
15 | 13 |
Equation 2:
Given:
- , (already filled)
- , (formula needs to be calculated in the box)
- Calculating for : So, when , .
To complete:
Let's choose additional values, such as and .
-
For : So, when , .
-
For : So, when , .
Now, the completed table for will be:
0 | 4 |
12 | -44 |
-1 | 8 |
5 | -16 |
If you need further details on any steps or explanations, feel free to ask!
Follow-up Questions
- How would you determine the slope and intercept from each equation?
- What is the significance of positive vs. negative slopes?
- How can you verify these points graphically?
- How does changing the slope or intercept affect the line's direction and position?
- What patterns do you notice in the y-values as x increases or decreases?
Tip: Remember, the slope represents how much changes with each increase of 1 in .
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Theorems
Slope-Intercept Form of a Line
Suitable Grade Level
Grades 7-9